Let I=(e^iα,e^iβ) be an analytic arc of the infinite Blaschke product B(z). We find some equivalent conditions under which the argument of B(e^iα+) or B(e^iβ-) is finite. As an application, we classify the analytic arcs of inner functions into four types.

The research is supported in part by the NNSF of China (Grant numbers 11831007, 11571099, 11371126). The first author is also supported by Hunan Provincial Innovation Foundation For Postgraduate (CX20190322).